Heisenberg’s Engagement with Plato and Malebranche on the path to 1925 Matrix Mechanics

          @misc{ pirsa_PIRSA:25100165,
            doi = {10.48660/25100165},
            url = {https://pirsa.org/25100165},
            author = {Gallus, Christoph},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Heisenberg{\textquoteright}s Engagement with Plato and Malebranche on the path to 1925 Matrix Mechanics},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100165 see, \url{https://pirsa.org}}
          }
          

Abstract

Heisenberg’s 1925 Matrizenmechanik (matrix mechanics) can be seen as a radical paradigm shift. While established scientists such as Bohr and Sommerfeld worked within the paradigm that electrons must be in a definite position at a definite time, the young Heisenberg abandoned these notions for electrons inside the atom. He wrote: > *“… in this situation it seems more advisable to give up completely any > hope of an observation of hitherto unobservable quantities (such as > position, orbital time of the electron) …”* > *“… it was not possible to assign a point in space (as a function of > time) to an electron by means of observable quantities …”* (W. Heisenberg, Über quantentheoretische Umdeutungen kinematischer und mechanischer Beziehungen, Zeitschrift für Physik, 33, pp. 880–881; received 29 July 1925.) Even radical ideas rarely occur in isolation. It is argued that Heisenberg’s early exposure to Plato’s philosophy and his discussions with friends on philosophical themes shaped by the Judeo-Christian tradition created fertile ground for his bold 1925 insight. The value of classical education was deeply rooted in his family: his father, a professor of Greek Philology, and his maternal grandfather, Nikolaus Wecklein—a noted scholar of Greek Sophists—ensured that classical education was a central pillar of his upbringing. Growing up in Würzburg and Munich, he read Latin and Greek, studied Kant’s Critique of Pure Reason at 16, and read Plato’s *Phaidon* and *Apology* in the original language. At 17, Plato’s *Timaios* introduced him to Greek atomist theory from a primary source. Lesser known is his exposure to French philosopher Malebranche, acknowledged when he later wrote: > “Robert’s remark about Malebranche had made it clear to me that > experience about atoms can only be of a rather indirect kind and that > atoms are likely not things.” (W. Heisenberg, Der Teil und das Ganze: Gespräche im Umkreis der Atomphysik, p. 21.) These two streams of thought may have aided Heisenberg's 1925 discovery because 1. they avoid a framework presupposing the independent existence of objects with definite positions at definite times, and 2. they offer a philosophy in which mathematics and abstract ideas can provide genuine insights about the world.